Last Wednesday I noticed a small spot on the base of his dorsal fin that was loosing it's color. On Friday it was twice the size of what it had been. I did a 50% water change the next morning, and all the levels are good. I wasn't home most of yesterday so I couldn't look at it then, but this morning, it's covering the full base of the top fin and he's now acting more lethargic than normal.

I can see a few areas on the tips of his fins that also look a little white, but since he's a crown tail I can't really tell if he's missing any of it or has any damage.

Housing
What size is your tank?
What temperature is your tank?
Does your tank have a filter?
Does your tank have an air stone or other type of aeration?
Is your tank heated?
What tank mates does your betta fish live with?

Food
What type of food do you feed your betta fish?
How often do you feed your betta fish?

Maintenance
How often do you perform a water change?
What percentage of the water do you change when you perform a water change?
What type of additives do you add to the water when you perform a water change?

Water Parameters:
Have you tested your water? If so, what are the following parameters?

Ammonia:
Nitrite:
Nitrate:
pH:
Hardness:
Alkalinity:

Symptoms and Treatment
How has your betta fish's appearance changed?
How has your betta fish's behavior changed?
When did you start noticing the symptoms?
Have you started treating your fish? If so, how?
Does your fish have any history of being ill?
How old is your fish (approximately)?

sorry about that, I have that picture in a bigger size, and a new one from today now, also in a bigger size.

today:

Housing
What size is your tank?5 gallons
What temperature is your tank? currently about 82*
Does your tank have a filter? yes
Does your tank have an air stone or other type of aeration? yes
Is your tank heated? yes
What tank mates does your betta fish live with? a very happy snail-yellow apple snail

Food
What type of food do you feed your betta fish? betta pellets and a freeze dry medley with daphnia, mysis shrimp and bloodworms
How often do you feed your betta fish? once a day

Maintenance
How often do you perform a water change? about once a week
What percentage of the water do you change when you perform a water change? between 25% and 50%
What type of additives do you add to the water when you perform a water change? the water conditioner to treat the tap water

Water Parameters:
Have you tested your water? not lately because it's been a well settled and cycled tank for almost 2 years now

Symptoms and Treatment
How has your betta fish's appearance changed? the color loss on his dorsal fin. it has gone from a small spot at the base of the fin to a large section of the fin and going down onto his body
How has your betta fish's behavior changed? he seems less active
When did you start noticing the symptoms? last Thursday
Have you started treating your fish? If so, how? we did an extra water change, but so far that's it
Does your fish have any history of being ill? no
How old is your fish (approximately)? we got him tiny about 4-6 months ago

no, they seem to be about the same as the rest, aside from the lack of color.

the color change has spread fairly quickly, last night there was not any color loss on his body, but this morning it was spread down, and the overall color loss has gone from barely noticeable to the size shown in the picture in less than a week...

It had been a bit longer than normal for our last water change, so there probably was a bit of a water problem, but it shouldn't have been bad enough to create a problem-we'd let it go longer before without any problems a few times.

My husband is convinced that it is fin rot, but it just doesn't really look like it to me, based on what I've been able to find about it.

I don't think it is fin rot. I am not experienced as I would like to be, I really wish I could help you. My suggestion is you directly PM Oldfishlady or another member of that caliber. She should know what to do.

Its hard for me to tell anything by the pic...however, I would go ahead and start a treatment for flex....

QT him in a small container that can be floated in the heated tank (attach it to the side so it doesn't sink or get knocked around by the filter)
Lower the water temp to 76-77F
Pre-mix some treatment water in a 1gal jug of dechlorinated water
Add 3tsp/gal Aquarium salt..dissolve and shake well before use
If you have any tannins to add to the treatment water..... all the better...this can be naturally dried and fallen from the tree oak leaf (10-12/gal crushed) or Indian almond leaf(1med-large/gal crushed) and steep for at least an hour before use...shake well
You can even use decaf green tea bag or blackwater extract for the tan water effect

Use this pre-mixed treatment water and make a 50% water change while he is in the QT container every 30 minutes times 3 and then 100% daily for the next 10 days...he needs to stay in this treatment water at the lower temps